Theorems · Theorem · functional analysis
SeminormFamily.finset_sup_comp
∀ {𝕜 : Type u_2} {𝕜₂ : Type u_3} {E : Type u_6} {F : Type u_7} {ι : Type u_9} [inst : NormedField 𝕜]
[inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E] [inst_3 : NormedField 𝕜₂] [inst_4 : AddCommGroup F]
[inst_5 : Module 𝕜₂ F] {σ₁₂ : 𝕜 →+* 𝕜₂} [inst_6 : RingHomIsometric σ₁₂] (q : SeminormFamily 𝕜₂ F ι) (s : Finset ι)
(f : E →ₛₗ[σ₁₂] F), (s.sup q).comp f = s.sup (q.comp f)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realproof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- Finsetstatement and proof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- RingHomstatement and proof · cited by 10,189
- NNReal.toRealproof · cited by 1,260
- NormedFieldstatement and proof · cited by 1,084
- Finset.supstatement and proof · cited by 530
- RingHomIsometricstatement and proof · cited by 282
- Seminormstatement · cited by 272
Cited by1
Results whose statement or proof uses this declaration.
- Seminorm.bound_comp_of_isInducingproof · cited by 1